Unitary Diagonalization and Quadratic Forms

James B. Carrell ()
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James B. Carrell: University of British Columbia, Department of Mathematics

Chapter Chapter 9 in Groups, Matrices, and Vector Spaces, 2017, pp 297-317 from Springer

Abstract: Abstract As we saw in Chap. 8 , when V is a finite-dimensional vector space over $${\mathbb {F}}$$ , then a linear mapping $$T:V\rightarrow V$$ is semisimple if and only if its eigenvalues lie in $${\mathbb {F}}$$ and its minimal polynomial has only simple roots. It would be useful to have a result that would allow one to predict that T is semisimple on the basis of a criterion that is simpler than finding the minimal polynomial, which, after all, requires knowing the roots of the characteristic polynomial.

Date: 2017
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DOI: 10.1007/978-0-387-79428-0_9

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